rut gon\
a, 2x [ 2x – 1 ] ^ 2 – 3x . ( x – 3 ) . ( x + 3 ) -4x . ( x + 1 )^2
b, ( a-b + c )^2 – ( b-c )^2 + 2ab – 2ac
c, ( 3x + 1 )^2 – 2.( 3x + 1 ) . ( 3x + 5 )
d, 4 . ( 3^2 + 1 ) . ( 3^4 + 1 ) . ( 3^8 + 1 ) . ( 3^16 + 1 ) . ( 3^32 + 1 )
rut gon\
a, 2x [ 2x – 1 ] ^ 2 – 3x . ( x – 3 ) . ( x + 3 ) -4x . ( x + 1 )^2
b, ( a-b + c )^2 – ( b-c )^2 + 2ab – 2ac
c, ( 3x + 1 )^2 – 2.( 3x + 1 ) . ( 3x + 5 )
d, 4 . ( 3^2 + 1 ) . ( 3^4 + 1 ) . ( 3^8 + 1 ) . ( 3^16 + 1 ) . ( 3^32 + 1 )
Đáp án:
$\begin{array}{l}
a)2x{\left( {2x – 1} \right)^2} – 3x\left( {x – 3} \right)\left( {x + 3} \right) – 4x{\left( {x + 1} \right)^2}\\
= 2x.\left( {4{x^2} – 4x + 1} \right) – 3x.\left( {{x^2} – 9} \right) – 4x\left( {{x^2} + 2x + 1} \right)\\
= 8{x^3} – 8{x^2} + 2x – 3{x^3} + 27x – 4{x^3} – 8{x^2} – 4x\\
= {x^3} – 16{x^2} + 25x\\
b){\left( {a – b + c} \right)^2} – {\left( {b – c} \right)^2} + 2ab – 2ac\\
= {\left[ {a – \left( {b – c} \right)} \right]^2} – {\left( {b – c} \right)^2} + 2a\left( {b – c} \right)\\
= {a^2} – 2.a.\left( {b – c} \right) + {\left( {b – c} \right)^2} – {\left( {b – c} \right)^2}\\
+ 2a\left( {b – c} \right)\\
= {a^2}\\
c){\left( {3x + 1} \right)^2} – 2\left( {3x + 1} \right).\left( {3x + 5} \right)\\
= 9{x^2} + 6x + 1 – 2.\left( {9{x^2} + 18x + 5} \right)\\
= 9{x^2} + 6x + 1 – 18{x^2} – 36x – 10\\
= – 9{x^2} – 30x – 9\\
d)4.\left( {{3^2} + 1} \right).\left( {{3^4} + 1} \right).\left( {{3^8} + 1} \right)\left( {{3^{16}} + 1} \right)\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^2} – 1} \right)\left( {{3^2} + 1} \right).\left( {{3^4} + 1} \right).\left( {{3^8} + 1} \right)\\
\left( {{3^{16}} + 1} \right)\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^4} – 1} \right)\left( {{3^4} + 1} \right).\left( {{3^8} + 1} \right)\left( {{3^{16}} + 1} \right)\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^8} – 1} \right)\left( {{3^8} + 1} \right)\left( {{3^{16}} + 1} \right)\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^{16}} – 1} \right)\left( {{3^{16}} + 1} \right)\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^{32}} – 1} \right).\left( {{3^{32}} + 1} \right)\\
= \dfrac{1}{2}.\left( {{3^{64}} – 1} \right)
\end{array}$
a, 2x(2x-1)² – 3x(x-3)(x+3) – 4x(x+1)²
= 2x(4x² – 4x +1) – 3x(x² – 9) – 4x(x² + 2x + 1)
= 8x³ – 8x² + 2x – 3x³ + 27x – 4x³ – 8x² – 4x
= x³ – 16x² + 25x
b, (a-b+c)² – (b-c)² + 2ab – 2ac
= (a-b)² + 2(a-b)c + c² – (b² – 2bc + c²) + 2ab – 2ac
= a² – 2ab + b² +2ac – 2bc + c² – b² + 2bc – c² + 2ab – 2ac
= a²
c, ( 3x + 1 )² – 2( 3x + 1 )( 3x + 5 )
= 9x² + 6x + 1 – 2(9x² + 18x + 5)
= 9x² + 6x + 1 – 18x² – 36x – 10
= -9x² -30x – 9
d, 4 . ( 3² + 1 )( 3^4 + 1 )( 3^8 + 1 )( 3^16 + 1 )( 3^32 + 1 )
=